defence exam Coast Guard Navik GD (General Duty) 02/2025 Mock Test Series Mathematics Permutations and Combinations Permutation Function and its properties
Let \( \alpha=\frac{(4!)!}{(4!)^{3!}}\ and \ \beta=\frac{(5!)!}{(5!)^{4!}}\). Then:
1
\( \alpha \in \mathrm{N}\) and \( \beta \notin \mathrm{N}\)
2
\( \alpha \notin \mathrm{N}\) and \( \beta \in \mathrm{N}\)
3
\(\alpha \in \mathrm{N}\) and \( \beta \in \mathrm{N}\)
4
\( \alpha \notin \mathrm{N}\) and \( \beta \notin \mathrm{N}\)